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BETON PRATEGANG TKS - 4023

Dr.Eng. Achfas Zacoeb, ST., MT.

Jurusan Teknik Sipil

Fakultas Teknik

Universitas Brawijaya

Session 10:

Composite Sections

Introduction

A composite section in context of prestressed concrete members

refers to a section with a precast member and cast-in-place (CIP)

concrete. There can be several types of innovative composite

sections. A few types are sketched in Fig. 1.

Figure 1. Examples of composite sections

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Introduction (cont’d)

Fig. 2 shows the reinforcement for the slab of a box girder bridge

deck with precast webs and bottom flange. The slab of the top

flange is cast on a stay-in formwork. The reinforcement of the slab

is required for the transverse bending of the slab. The reinforcement

at the top of the web is required for the horizontal shear transfer.

Figure 2. Girder bridge deck with precast webs and

bottom flange and CIP slab

Introduction (cont’d)

The advantages of composite construction are as follows :

1. Savings in form work

2. Fast-track construction

3. Easy to connect the members and achieve continuity.

The prestressing of composite sections can be done in stages. The

precast member can be first pre-tensioned or post-tensioned at the

casting site. After the cast-in-place (cast-in-situ) concrete achieves

strength, the section is further post-tensioned. The grades of

concrete for the precast member and the cast-in-place portion may

be different. In such a case, a transformed section is used to

analyze the composite section.

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Analysis

The analysis of a composite section depends upon the type of

composite section, the stages of prestressing, the type of

construction and the loads. The type of construction refers to

whether the precast member is propped or unpropped during the

casting of the CIP portion. If the precast member is supported by

props along its length during the casting, it is considered to be

propped. Else, if the precast member is supported only at the ends

during the casting, it is considered to be unpropped.

Fig. 3 shows a composite section with precast web and cast-in-

place flange. The web is prestressed before the flange is cast. At

transfer and after casting of the flange (before the section behaves

like a composite section), the following are the stress profiles for the

precast web.

Analysis (cont’d)

Figure 3. Stress profiles for the precast web

Where:

P0 = prestress at transfer after short term losses

Pe = effective prestress during casting of flange after long term

losses

MSW = moment due to self weight of the precast web

MCIP = moment due to weight of the CIP flange.

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Analysis (cont’d)

At transfer, the loads acting on the precast web are P0 and MSW. By

the time the flange is cast, the prestress reduces to Pe due to long

term losses. In addition to Pe and MSW, the web also carries MCIP.

The width of the flange is calculated based on the concept of

effective flange width.

At service (after the section behaves like a composite section), the

stress profiles for the full depth of the composite section are shown

in Fig. 4.

Analysis (cont’d)

Figure 4. Stress profiles for the composite section

Here, MLL is the moment due to live load. If the precast web is

unpropped during casting of the flange, the section does not

behave like a composite section to carry the prestress and self

weight.

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Analysis (cont’d)

Hence, the stress profile due to Pe + MSW

+ MCIP is terminated at the

top of the precast web. If the precast web is propped during casting

and hardening of the flange, the section behaves like a composite

section to carry the prestress and self weight after the props are

removed. The stress profile is extended up to the top of the flange.

When the member is placed in service, the full section carries MLL.

Analysis (cont’d)

From the analyses at transfer and under service loads, the stresses

at the extreme fibres of the section for the various stages of loading

are evaluated. These stresses are compared with the respective

allowable stresses.

Stress in precast web at transfer:

(1)

Stress in precast web after casting of flange:

(2)

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Analysis (cont’d)

Stress in precast web at service:

a. For unpropped construction

(3)

b. For propped construction

(4)

where:

A = area of the precast web

c = distance of edge from CGC of precast web

c / = distance of edge from CGC of composite section

e = eccentricity of CGS

I = moment of inertia of the precast web

I / = moment of inertia of the composite section.

Analysis (cont’d)

From the analysis for ultimate strength, the ultimate moment

capacity is calculated. This is compared with the demand under

factored loads. The analysis at ultimate is simplified by the following

assumptions:

1. The small strain discontinuity at the interface of the precast and

CIP portions is ignored.

2. The stress discontinuity at the interface is also ignored.

3. If the CIP portion is of low grade concrete, the weaker CIP

concrete is used for calculating the stress block.

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Analysis (cont’d)

The strain and stress diagrams and the force couples at ultimate

are shown in Fig. 5.

Figure 5. Sketches for analysis at ultimate

Analysis (cont’d)

The variables in Fig. 5 are explained as follows: bf

= width of the flange

bw = width of the web

Df = depth of the flange

d = depth of the centroid of prestressing steel (CGS)

Ap = area of the prestressing steel

Δεp = strain difference for the prestressing steel

xu = depth of the neutral axis at ultimate

εpu = strain in prestressing steel at the level of CGS at ultimate

fpu = stress in prestressing steel at ultimate

fck = characteristic compressive strength of the weaker concrete

Cuw = resultant compression in the web (includes portion of flange

above precast web)

Cuf = resultant compression in the outstanding portion of flange

Tuw = portion of tension in steel balancing Cuw

Tuf = portion of tension balancing Cuf

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Analysis (cont’d)

The expressions of the forces are as follows:

(5)

(6)

(7)

(8)

The symbols for the areas of steel are as follows: Apf

= part of Ap that balances compression in the outstanding flanges

Apw = part of Ap

that balances compression in the web

Analysis (cont’d)

The equilibrium equations are given in Eq. 9, these equations

already explained in Section Analysis of Members under Flexure.

The ultimate moment capacity (MuR) is calculated from Eq. 10.

(9)

(10)

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Design

The design is based on satisfying the allowable stresses under

service loads and at transfer. The section is then analyzed for

ultimate loads to satisfy the limit state of collapse. The member is

also checked to satisfy the criteria of limit states of serviceability,

such as deflection and crack width (for Type 3 members only).

Before the calculation of the initial prestressing force (P0) and the

eccentricity of the CGS (e) at the critical section, the type of

composite section and the stages of prestressing need to be

decided. Subsequently, a trial and error procedure is adopted for

the design.

Design (cont’d)

The following steps explain the design of a composite section with

precast web and cast-in-place flange. The precast web is

prestressed before the casting of the flange. The member is

considered to be Type 1 member.

Step 1. Compute e.

With a trial section of the web, the CGS can be located at the

maximum eccentricity (emax). The maximum eccentricity is

calculated based on zero stress at the top of the precast web. This

gives an economical solution. The following stress profile is used to

determine emax (for the details can be shown in Fig. 6).

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Design (cont’d)

Figure 6. Stress profile for maximum eccentricity of CGS

where:

CGC = centroid of the precast web

kb = distance of the bottom kern of the precast web from CGC

Msw = moment due to self weight of the precast web.

P0 = a trial prestressing force at transfer.

Design (cont’d)

Step 2. Compute equivalent moment for the precast web.

A moment acting on the composite section is transformed to an

equivalent moment for the precast web. This is done to compute the

stresses in the precast web in terms of the properties of the precast

web itself and not of the composite section.

For a moment Mc which acts after the section behaves like a

composite section, the stresses in the extreme fibres of the precast

web are determined from the following stress profile as shown in

Fig. 7.

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Design (cont’d)

Figure 7. Stress profile for the composite section

Design (cont’d)

(11)

(12)

where: CGC’ = centroid of the composite section

ct’ = distance of the top of the precast web from the CGC’

ct” = distance of the top of the composite section from the CGC’.

cb’ = distance of the bottom of the precast web (or composite section)

from the CGC’

I ’ = moment of inertia for the composite section.

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Design (cont’d)

The following quantities are defined as the ratios of the properties of

the precast web and composite section as follows:

(13)

(14)

Then the stresses in the extreme fibres of the precast web can be

expressed in terms of mt and mb as follows:

Design (cont’d)

(15)

(16)

where: A = area of the precast web

kb = distance of the bottom kern of the precast web from CGC

kt = distance of the top kern of the precast web from CGC

The quantities mt Mc and mb Mc

are the equivalent moments. Thus,

the stresses in the precast web due to Mc are expressed in terms of

the properties of the precast web itself.

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Design (cont’d)

Step 3. Compute Pe

Let MP be the moment acting on the precast web prior to the section

behaving like a composite section. After Mc is applied on the

composite section, the total moment for the precast web is MP +

mbMc.

The stress at the bottom for Type 1 member due to service loads is

zero. Therefore,

or (17)

Note that the prestressing force is acting only on the precast web

and hence, e is the eccentricity of the CGS from the CGC of the

precast web.

Design (cont’d)

Step 4. Estimate P0 as follows.

a. 90% of the initial applied prestress (Pi) for pre-tensioned

members.

b. Equal to Pi for post-tensioned members.

The value of Pi is estimated as follows.

(18)

(19)

Revise e, the location of CGS, as given in Step 1 based on the new

value of P0.

(20)

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Design (cont’d)

Step 5. Check for the compressive stresses in the precast web.

At transfer, the stress at the bottom is given as follows:

(21)

The stress fb should be limited to fcc,all, where fcc,all

is the allowable

compressive stress in concrete at transfer.

At service,

(22)

The stress ft should be limited to fcc,all, where fcc,all

is the allowable

compressive stress in concrete under service loads. If the stress

conditions are not satisfied, increase A.

Design (cont’d)

Step 6. Check for the compressive stress in the CIP flange

(23)

The stress ft/ should be limited to fcc,all, where fcc,all

is the allowable

compressive stress in concrete under service loads.

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Analysis of Horizontal Shear Transfer

With increase in the load, the bottom face of the CIP portion tends

to slip horizontally and move upwards with respect to the top face of

the precast portion. To prevent this and to develop the composite

action, shear connectors in the form of shear friction

reinforcement is provided.

The required shear friction reinforcement (per metre span) is

calculated as follows:

(24)

The minimum requirements of shear friction reinforcement and

spacing are similar to that for shear reinforcement in the web.

Analysis of Horizontal Shear

Transfer (cont’d)

In Eq. (24), where : Asv

= area of shear friction reinforcement in mm2/m

bv = width of the interface of precast and CIP portions

h = horizontal shear stress at the interface in N/mm2

fy = yield stress in N/mm2

= coefficient of friction

= 1.0 for intentionally roughened interface with normal weight concrete

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Analysis of Horizontal Shear

Transfer (cont’d)

The shear reinforcement in the web can be extended and anchored

in the CIP portion to act as shear friction reinforcement, as shown in

Fig . 8.

Figure 8. Shear reinforcement used for shear transfer

Problem Example

The mid-span section of a composite beam is

shown in the figure. The precast web 300 mm

× 920 mm (depth) is post-tensioned with an

initial force (P0) of 2450 kN. The effective

prestress (Pe) is estimated as 2150 kN.

Moment due to the self weight of the precast

web (MSW) is 270 kNm at mid-span.

After the web is erected in place, the top slab of 150 mm ×

920 mm (width) is casted (unpropped) producing a moment

(MCIP) of 135 kNm. After the slab concrete has hardened, the

composite section is to carry a maximum live load moment (MLL)

of 720 kNm.

Compute stresses in the section at various stages!

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Problem Example (cont’d)

Solution

1. Calculation of geometric properties.

Precast web

A = 2.76 × 105 mm2

I = 1.95 × 1010 mm2

CGC from bottom = 460 mm.

Composite section

A/ = 4.14 × 105 mm2

I / = 4.62 × 1010 mm2

CGC/ from bottom = 638 mm.

Problem Example (cont’d)

2. Calculation of stresses in web at transfer

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Problem Example (cont’d)

3. Calculation of stresses in web after long term losses

Problem Example (cont’d)

4. Calculation of stresses in web after casting of flange

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Problem Example (cont’d)

5. Calculation of stresses in the composite section at service

Stress due to MLL

At top fibre At bottom fibre

At top fibre of precast web, the stress due to MLL is calculated

from proportionality of triangles.

Problem Example (cont’d)

Total stress in precast web:

At top fibre At bottom fibre

ft = – 4.16 – 4.57 fb = – 11.42 + 10.36

= – 8.73 N/mm2 = – 1.06 N/mm2

Total stress in CIP slab (due to MLL only):

At top fibre At bottom fibre

fb / = – 4.57 N/mm2 ft

/ = – 7.01 N/mm2

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Problem Example (cont’d)

Stress profiles:

Exercise

The mid-span section of a composite beam

with the length of beam, L = 2X m is shown in

the figure. The precast web 3X0 mm × 9X0

mm (depth) is post-tensioned with an initial

force (P0) of 24X0 kN. The effective prestress

(Pe) is estimated as 21X0 kN. The self weight

of the precast web (QSW) is 255 N/m3.

After the web is erected in place, the top slab of 1X0 mm ×9X0 mm

(width) is casted (unpropped) producing a self weight (QCIP) of 240

N/m3. After the slab concrete has hardened, the composite section

is to carry a maximum uniform live load (QLL) of 40 N/m.

Compute stresses in the section at various stages!

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Thanks for Your Attention

and

Success for Your Study!